Differentiation is the key

By that I mean - you have to make yourself different in some meaningful way from every other cleaner. If you don't then you will end up competing on price which means you either lose out or make smaller/no profits. Once your clients have a reason to use you - and only you - then you have the makings of a successful business.
I work in London which is full of low priced cleaners. Do a google search for carpet cleaning London and you will get through hundreds of pages of listings before you find my site. The competition for work is very high. My view was that to get the high price work in my area I have to be different than all those other people, otherwise I am just one of many. I have done that and for this year so far I am working on 95% repeat clients and 5% recommendations. So what happens on the other hundreds of pages of internet listings is irrelevant.
So my comment to Mr Happy Monday is that you are looking at this the wrong way round. You are asking Derek to be the same as you. You want him to charge the same price for the same service to make the playing field level. What he has done is differentiated himself by offering "affordable" cleaning. i.e., a good job at a low price. You need to think more about what differentiates you from all the other cleaners in the area. When you have successfully done that you will never need to bother about anyone else's marketing again.
Nigel